Hi @lampix,
No idea mate! I have ended using the TinyGSM library as writing everything as pure AT commands was taking way to long.
I just had a look and it seems that TinyGSM does support a bunch of modems including SIM7060. I would need to look in depth at the .h file to see if there is something majorly different to the SIM800L (there's 800+ lines of code! :0)
It would be easier if I had that specific module with me so I could test instantly, let's continue the chat over email and we'll figure something out.